The theory of nonlinear, complex systems has become by now a proven problem-solving approach in the natural sciences. And it is now also recognized that many if not most of our social, ecological, economical and political problems are essentially of a global, complex and nonlinear nature. And it is now further accepted than any holistic perspective of the human mind and brain can hardly be achieved by any other approach. In this wide-ranging, scholarly but very concise treatment, physicist, computer scientist and philosopher klaus mainzer discusses, in essentially nontechnical language, the common framework behind these ideas and challenges. Emphasis is given to the evolution of new structures in natural and cultural systems and we are lead to see clearly how the new integrative approach can give insights not available from traditional reductionistic methods. The fifth edition enlarges and revises almost all sections and supplements an entirely new chapter on the complexity of economic systems. From the reviews of the fourth "this book is ambitious, incredibly erudite with 22 pages of references, and is indisputably clearly and beautifully written and illustrated. It is perfectly suited to a first course on the science of complexity. Even beginners and young graduate students will have something to learn from this book." (andre hautot, physicalia, vol. 57 (3), 2005) "all-in-all, this highly recommended book is a wonderful resource for intuitive basic ideas in the need of rigorous formulation." (albert a. Mullin, zentralblatt math, vol. 1046, 2004) "readers of this book will enjoy mainzer's exposition, which is based on a tight coupling between classical and historical concepts from plato and aristotle to modern, mathematical and physical developments . Every chapter begins with a section designed to orient the reader to the perspective of philosophical developments through the ages pertinent to the topic at hand.

Review:

Chaos is cropping up everywhere these days. As it becomes ever more apparent that Newtonian mechanics is inadequate for modeling nonlinear systems, or systems that have too many degrees of freedom to handle easily, researchers in all fields are turning toward nonlinear dynamics as a refreshing alternative. This is a paradigm shift � la Kuhn, and Klaus Mainzer guides us through it with an astounding range of historical and scientific knowledge. From quantum physics to consciousness to economics, Mainzer shows us how thinking complexly can solve problems over which standard, linear thinking continually stumbles. Instead of simplifying, however, Mainzer revels in the complexity of complexity, so the reader should be prepared for advanced concepts in such varied fields as mathematics, physics, and economics. Difficult, but worthwhile reading.

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